Function Operations, Compositions, and Inverses

Front

Define function addition.

Back

Function addition is the operation of combining two functions, f(x) and g(x), to create a new function (f + g)(x) = f(x) + g(x).

Front

What is the formula for function subtraction?

Back

Function subtraction is defined as (f - g)(x) = f(x) - g(x).

Front

How do you find the composition of two functions?

Back

The composition of two functions f and g is denoted as (f ∘ g)(x) = f(g(x)).

Front

What is the inverse of a function?

Back

The inverse of a function f, denoted as f^{-1}, is a function that reverses the effect of f, such that f(f^{-1}(x)) = x.

Front

Given f(x) = 2x + 3, find f(2).

Back

f(2) = 2(2) + 3 = 7.

Front

If f(x) = x^2, what is f(3)?

Back

f(3) = 3^2 = 9.

Front

What is the result of (f + g)(x) if f(x) = x^2 and g(x) = 2x?

Back

(f + g)(x) = x^2 + 2x.

Front

Calculate (f - g)(x) for f(x) = 3x + 5 and g(x) = x - 2.

Back

(f - g)(x) = (3x + 5) - (x - 2) = 2x + 7.

Front

What is the product of two functions f(x) = x and g(x) = x + 1?

Back

(f ⋅ g)(x) = x(x + 1) = x^2 + x.

Front

Find the inverse of f(x) = 3x - 6.

Back

To find the inverse, set y = 3x - 6, then solve for x: x = (y + 6)/3, so f^{-1}(x) = (x + 6)/3.